Wave

Type of Wave 2006

# Which one of the following statement is true? (2006)

1 Both light and sound waves can travel in vacuum

2 Both light and sound waves in air are transverse

3 The sound waves in air are longitudinal while the

light waves are transverse

4 Both light and sound waves in air are longitudinal

 Wave Equation 2013, 2012, 2011,
𝑦 = 𝐴 sin 𝑘𝑥 + 𝑡 2010, 2009
𝑉max particle = 𝐴
𝑉wave = /𝑘

# A wave travelling in the +ve x-direction having displacement along y-direction

as 1m, wavelength 2 m and frequency of 1/ Hz is represented by: (2013)

1 y = sin (2x + 2t)

2 y = sin (x – 2t)

3 y = sin (2x – 2t)

4 y = sin (10x – 20t)

Question (Wave Equation)


# The equation of a simple harmonic wave is given by y = 3 sin (50t – x) where x
2
and y are in metres and t is in seconds. The ratio of maximum particle velocity to
the wave velocity is: (2012 Mains)

1 2

2 3/2

3 3

4 2/3
 Phase Difference between two waves 2011, 2004
 = 1 – 2

𝑥
# The phase difference between two waves, represented by: y1 = 10–6 sin (100t + + 0.5)m
50
𝑥
and y2 = 10–6 cos (100t + )m, where x is expressed in meters and t is expressed in seconds,
50
is approximately.

1 2.07 radians

2 0.5 radians

3 1.5 radians

4 1.07 radians
 Propagation of Wave from one medium to another 2011
 𝑣
= , ′
𝑣 = , 𝑓 = same
 

# Sound wave travels at 350 m/s through a warm air and at 3500 m/s through brass. The
wavelength of a 700 Hz acoustic wave as it enters brass from air

1 Decreases by a factor 10

2 Increases by a factor 20

3 Increases by a factor 10

4 Decreases by a factor 20
 Intensity of Source 2005
Point Source Line Source
1 1
𝐼 2 𝐼 2
𝑟 𝑟
Iplane  r0

# A point source emits sound equally in all directions in a non-absorbing medium. Two
point P and Q are at distance of 2m and 3m respectively from the source. The ratio of the
intensities of the waves at P and Q is: [MR*] (2005)

1 9:4

2 2:9

3 9:2

4 4:9
 Speed of Wave in String 2022, 2016
𝑇 𝑇
𝑉= =
 𝐴

# A uniform rope of length L and mass m1 hangs vertically from a rigid support. A
block of mass m2 is attached to the free end of the rope. A transverse pulse of
wavelength 1 is produced at the lower end of the rope. The wavelength of the
pulse when it reaches the top of the rope is 2. The ratio 2/ 1 is: [MR*] (2016-I)

𝑚1 𝑚1 + 𝑚2
1 2
𝑚2 𝑚2

𝑚2 𝑚1 + 𝑚2
3 4
𝑚1 𝑚1
Question (Wave in String)

# If the initial tension on a stretched string is doubled, then the ratio of the initial
and final speed of a transverse wave along the string is: (2022)

1 1:2

2 1:1

3 2:1

4 1: 2
 Interference 2008
2
𝐼max = 𝐼1 + 𝐼2
2
𝐼min = 𝐼1 − 𝐼2

# Two periodic waves of intensities I1 and I2 pass through a region at the same time in the
same direction. The sum of the maximum and minimum intensities is (2008)

1 𝐼1 − 𝐼2

2 2 𝐼1 + 𝐼2

3 𝐼1 + 𝐼2

2
4 𝐼1 − 𝐼2
Organ Pipe 2024, 2023, 2023-M,
2022 (R), 2022, 2018,
𝑛𝑉 nth harmonic (n – 1) 2017
𝐹open = overtone
2𝐿

2𝑛 + 1 𝑉 nth overtone (2n + 1) 2016, 2015, 2014

𝐹close = harmonic
2𝐿
Question (Organ Pipe)

# The 4th overtone of a closed organ pipe is same as that of 3rd overtone open
pipe. The ratio of the length of the closed pipe to the length of the open pipe is:
(2023-Manipur)
1 8:9

2 9:7

3 9:8

4 7:9
Question (Organ Pipe)

# An organ pipe filled with a gas at 27°C resonates at 400 Hz in its fundamental
mode. If it is filled with the same gas at 90°C, the resonance frequency at the
same mode will be: (2022 Re)

1 512 Hz

2 420 Hz

3 440 Hz

4 484 Hz
Question (Organ Pipe)

# The two nearest harmonics of a tube closed at one end and open at other end
are 220 Hz and 260 Hz. What is the fundamental frequency of the system?
(2017-Delhi)
1 20 Hz

2 30 Hz

3 40 Hz

4 10 Hz
 Sonometre Wire 2020, 2015
𝑛𝑉
𝑓=
2𝑙

# The length of the string of a musical instrument is 90 cm and has a fundamental

frequency of 120 Hz. Where should it be pressed to produce fundamental
frequency of 180 Hz? (2020-Covid)

1 60 cm

2 45 cm

3 80 cm

4 75 cm
Question (Sonometer Wire)

# If n1, n2 and n3 are the fundamental frequencies of three segments into which a
string is divided, then the original fundamental frequency n of the string is given
by: (2014)
1 1 1 1
1 = + +
𝑛 𝑛1 𝑛2 𝑛3

1 1 1 1
2 = + +
𝑛 𝑛1 𝑛2 𝑛3

3 𝑛 = 𝑛1 + 𝑛2 + 𝑛3

4 𝑛 = 𝑛1 + 𝑛2 + 𝑛3
 Resonance Tube 2016
 = 𝟐 𝒍𝟐 − 𝒍𝟏
𝒗 = 𝒇

# An air column, closed at one end and open at the other, resonates with a tuning
fork when the smallest length of the column is 50 cm. The next larger length of
the column resonating with the same tuning fork is: (2016-I)

1 66.7 cm

2 100 cm

3 150 cm

4 200 cm
Question

# A tunning fork is used to produce resonance in a glass tube. The length of air
column in this tube can be adjusted by a variable piston. At room temperature of
27°C two successive resonances are produced at 20 cm and 73 cm of column
length. If the frequency of the tunning fork is 320 Hz, the velocity of sound in air
at 27°C is

1 350 m/s

2 339 m/s

3 330 m/s

4 350 m/s
Beats
Frequency Difference
2020, 2016, 2013, 2011,
2010, 2009
Tension Increase →f
Waxing →f
Sharping →f
Question (Beats)

# In a guitar, two strings A and B made of same material are slightly out of tune
and produce beats of frequency 6 Hz. When tension in B is slightly decreased, the
beat frequency increases to 7 Hz. If the frequency of A is 530 Hz, the original
frequency of B will be: [MR*] (2020)

1 524 Hz

2 536 Hz

3 537 Hz

4 523 Hz
Question (Beats)

# A source of unknown frequency gives 4 beats/s, when sounded with a source of

known frequency 250 Hz. The second harmonic of the source of unknown
frequency gives five beats per second, when sounded with a source of frequency
513 Hz. The unknown frequency is: (2013)

1 260 Hz

2 254 Hz

3 246 Hz

4 240 Hz
Question (Beats)

# Two sources of sound placed close to each other are emitting progressive
waves given by y1 = 4 sin 600 t and y2 = 5 sin 608 t. An observer located near
these two sources of sound will hear: [MR*] (2012 Pre)

1 4 beats per second with intensity ratio 25 : 16 between waxing and waning.

2 8 beats per second with intensity ratio 25 : 16 between waxing and waning.

3 8 beats per second with intensity ratio 81 : 1 between waxing and waning.

4 4 beats per second with intensity ratio 81 : 1 between waxing and waning.
Question (Beats)

# Each of the two strings of length 51.6 cm and 49.1 cm are tensioned separately
by 20 N force. Mass per unit length of both the strings is same and equal to 1 g/m.
When both the strings vibrate simultaneously the number of beats is: (2009)

1 7

2 8

3 3

4 5
Question (Beats)

# Two points are located at a distance of 10 m and 15 m from the source of oscillation.
The period of oscillation is 0.05 sec and the velocity of the wave is 300 m/sec. What is
the phase difference between the oscillation of two points? (2008)

1 /6

2 /3

3 2/3

4 